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          数据结构算法Day05-栈
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            <div class="post-description">数据结构算法打卡，参考的王铮老师在极客时间上的《数据结构与算法之美》<br> <img src="https://static001.geekbang.org/resource/image/79/aa/79d1a08a0a016b4648a764fc62bed8aa.jpg"></div>

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        <h1 id="1-概念"><a href="#1-概念" class="headerlink" title="1.概念"></a>1.概念</h1><p>栈是一种“操作受限”的线性表，只允许在一端插入和删除数据，后进者先出，先进者后出，这就是典型的“栈”结构。</p>
<p><img src="https://static001.geekbang.org/resource/image/3e/0b/3e20cca032c25168d3cc605fa7a53a0b.jpg" alt="img"></p>
<p>当某个数据集合只涉及在一端插入和删除数据，并且满足后进先出、先进后出的特性，我们就应该首选“栈”这种数据结构。</p>
<h1 id="2-如何实现一个栈"><a href="#2-如何实现一个栈" class="headerlink" title="2.如何实现一个栈"></a>2.如何实现一个栈</h1><p>实际上，栈既可以用数组来实现，也可以用链表来实现。用数组实现的栈，我们叫作<strong>顺序栈</strong>，用链表实现的栈，我们叫作<strong>链式栈</strong>。</p>
<p>空间复杂度：O(1)</p>
<p>时间复杂度：O(1)</p>
<p>java实现</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br></pre></td><td class="code"><pre><span class="line"></span><br><span class="line"><span class="comment">// 基于数组实现的顺序栈</span></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">ArrayStack</span> </span>&#123;</span><br><span class="line">  <span class="keyword">private</span> String[] items;  <span class="comment">// 数组</span></span><br><span class="line">  <span class="keyword">private</span> <span class="keyword">int</span> count;       <span class="comment">// 栈中元素个数</span></span><br><span class="line">  <span class="keyword">private</span> <span class="keyword">int</span> n;           <span class="comment">//栈的大小</span></span><br><span class="line"></span><br><span class="line">  <span class="comment">// 初始化数组，申请一个大小为n的数组空间</span></span><br><span class="line">  <span class="function"><span class="keyword">public</span> <span class="title">ArrayStack</span><span class="params">(<span class="keyword">int</span> n)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">this</span>.items = <span class="keyword">new</span> String[n];</span><br><span class="line">    <span class="keyword">this</span>.n = n;</span><br><span class="line">    <span class="keyword">this</span>.count = <span class="number">0</span>;</span><br><span class="line">  &#125;</span><br><span class="line"></span><br><span class="line">  <span class="comment">// 入栈操作</span></span><br><span class="line">  <span class="function"><span class="keyword">public</span> <span class="keyword">boolean</span> <span class="title">push</span><span class="params">(String item)</span> </span>&#123;</span><br><span class="line">    <span class="comment">// 数组空间不够了，直接返回false，入栈失败。</span></span><br><span class="line">    <span class="keyword">if</span> (count == n) <span class="keyword">return</span> <span class="keyword">false</span>;</span><br><span class="line">    <span class="comment">// 将item放到下标为count的位置，并且count加一</span></span><br><span class="line">    items[count] = item;</span><br><span class="line">    ++count;</span><br><span class="line">    <span class="keyword">return</span> <span class="keyword">true</span>;</span><br><span class="line">  &#125;</span><br><span class="line">  </span><br><span class="line">  <span class="comment">// 出栈操作</span></span><br><span class="line">  <span class="function"><span class="keyword">public</span> String <span class="title">pop</span><span class="params">()</span> </span>&#123;</span><br><span class="line">    <span class="comment">// 栈为空，则直接返回null</span></span><br><span class="line">    <span class="keyword">if</span> (count == <span class="number">0</span>) <span class="keyword">return</span> <span class="keyword">null</span>;</span><br><span class="line">    <span class="comment">// 返回下标为count-1的数组元素，并且栈中元素个数count减一</span></span><br><span class="line">    String tmp = items[count-<span class="number">1</span>];</span><br><span class="line">    --count;</span><br><span class="line">    <span class="keyword">return</span> tmp;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h1 id="3-支持动态扩容的顺序栈"><a href="#3-支持动态扩容的顺序栈" class="headerlink" title="3.支持动态扩容的顺序栈"></a>3.支持动态扩容的顺序栈</h1><p>数组： 重新申请更大的空间，将原来的数组拷贝过去</p>
<p>链表：没有限制，但是浪费空间</p>
<p><img src="https://static001.geekbang.org/resource/image/b1/da/b193adf5db4356d8ab35a1d32142b3da.jpg" alt="img"></p>
<h1 id="4-栈在函数调用中的应用"><a href="#4-栈在函数调用中的应用" class="headerlink" title="4.栈在函数调用中的应用"></a>4.栈在函数调用中的应用</h1><h2 id="应用1：函数调用栈"><a href="#应用1：函数调用栈" class="headerlink" title="应用1：函数调用栈"></a>应用1：函数调用栈</h2><p>操作系统给每个线程分配了一块独立的内存空间，这块内存被组织成“栈”这种结构, 用来存储函数调用时的临时变量。每进入一个函数，就会将临时变量作为一个栈帧入栈，当被调用函数执行完成，返回之后，将这个函数对应的栈帧出栈。</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line">   <span class="keyword">int</span> a = <span class="number">1</span>; </span><br><span class="line">   <span class="keyword">int</span> ret = <span class="number">0</span>;</span><br><span class="line">   <span class="keyword">int</span> res = <span class="number">0</span>;</span><br><span class="line">   ret = add(<span class="number">3</span>, <span class="number">5</span>);</span><br><span class="line">   res = a + ret;</span><br><span class="line">   printf(<span class="string">"%d"</span>, res);</span><br><span class="line">   reuturn <span class="number">0</span>;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">add</span><span class="params">(<span class="keyword">int</span> x, <span class="keyword">int</span> y)</span> </span>&#123;</span><br><span class="line">   <span class="keyword">int</span> sum = <span class="number">0</span>;</span><br><span class="line">   sum = x + y;</span><br><span class="line">   <span class="keyword">return</span> sum;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p>从代码中我们可以看出，main() 函数调用了 add() 函数，获取计算结果，并且与临时变量 a 相加，最后打印 res 的值。为了让你清晰地看到这个过程对应的函数栈里出栈、入栈的操作，我画了一张图。图中显示的是，在执行到 add() 函数时，函数调用栈的情况。</p>
<p><img src="https://static001.geekbang.org/resource/image/17/1c/17b6c6711e8d60b61d65fb0df5559a1c.jpg" alt="img"></p>
<h2 id="应用2：表达式求值中的应用"><a href="#应用2：表达式求值中的应用" class="headerlink" title="应用2：表达式求值中的应用"></a>应用2：表达式求值中的应用</h2><p>算术表达式简化为只包含加减乘除四则运算，比如：34+13*9+44-12/3。</p>
<p>实际上，编译器就是通过两个栈来实现的。其中一个保存操作数的栈，另一个是保存运算符的栈。我们从左向右遍历表达式，当遇到数字，我们就直接压入操作数栈；当遇到运算符，就与运算符栈的栈顶元素进行比较。</p>
<p>如果比运算符栈顶元素的优先级高，就将当前运算符压入栈；如果比运算符栈顶元素的优先级低或者相同，从运算符栈中取栈顶运算符，从操作数栈的栈顶取 2 个操作数，然后进行计算，再把计算完的结果压入操作数栈，继续比较。</p>
<p>我将 3+5*8-6 这个表达式的计算过程画成了一张图，你可以结合图来理解我刚讲的计算过程。</p>
<p><img src="https://static001.geekbang.org/resource/image/bc/00/bc77c8d33375750f1700eb7778551600.jpg" alt="img"></p>
<h2 id="应用3：在括号场景的使用"><a href="#应用3：在括号场景的使用" class="headerlink" title="应用3：在括号场景的使用"></a>应用3：在括号场景的使用</h2><p>判断括号是否合法</p>
<p>比如，{[] ()[{}]}或[{()}([])]等都为合法格式，而{[}()]或[({)]为不合法的格式。</p>
<p>我们用栈来保存未匹配的左括号，从左到右依次扫描字符串。当扫描到左括号时，则将其压入栈中；当扫描到右括号时，从栈顶取出一个左括号。如果能够匹配，比如“(”跟“)”匹配，“[”跟“]”匹配，“{”跟“}”匹配，则继续扫描剩下的字符串。如果扫描的过程中，遇到不能配对的右括号，或者栈中没有数据，则说明为非法格式。</p>
<p>当所有的括号都扫描完成之后，如果栈为空，则说明字符串为合法格式；否则，说明有未匹配的左括号，为非法格式。</p>

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